- FindStat

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Identifier

St001894: Signed permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>0
[-1]=>1
[1,2]=>0
[1,-2]=>2
[-1,2]=>1
[-1,-2]=>3
[2,1]=>1
[2,-1]=>2
[-2,1]=>2
[-2,-1]=>2
[1,2,3]=>0
[1,2,-3]=>3
[1,-2,3]=>2
[1,-2,-3]=>5
[-1,2,3]=>1
[-1,2,-3]=>4
[-1,-2,3]=>3
[-1,-2,-3]=>6
[1,3,2]=>1
[1,3,-2]=>3
[1,-3,2]=>3
[1,-3,-2]=>4
[-1,3,2]=>2
[-1,3,-2]=>4
[-1,-3,2]=>4
[-1,-3,-2]=>5
[2,1,3]=>1
[2,1,-3]=>4
[2,-1,3]=>2
[2,-1,-3]=>5
[-2,1,3]=>2
[-2,1,-3]=>5
[-2,-1,3]=>2
[-2,-1,-3]=>5
[2,3,1]=>2
[2,3,-1]=>3
[2,-3,1]=>4
[2,-3,-1]=>4
[-2,3,1]=>3
[-2,3,-1]=>3
[-2,-3,1]=>4
[-2,-3,-1]=>5
[3,1,2]=>2
[3,1,-2]=>4
[3,-1,2]=>3
[3,-1,-2]=>4
[-3,1,2]=>3
[-3,1,-2]=>4
[-3,-1,2]=>3
[-3,-1,-2]=>5
[3,2,1]=>2
[3,2,-1]=>3
[3,-2,1]=>4
[3,-2,-1]=>4
[-3,2,1]=>3
[-3,2,-1]=>3
[-3,-2,1]=>4
[-3,-2,-1]=>5
[1,2,3,4]=>0
[1,2,3,-4]=>4
[1,2,-3,4]=>3
[1,2,-3,-4]=>7
[1,-2,3,4]=>2
[1,-2,3,-4]=>6
[1,-2,-3,4]=>5
[1,-2,-3,-4]=>9
[-1,2,3,4]=>1
[-1,2,3,-4]=>5
[-1,2,-3,4]=>4
[-1,2,-3,-4]=>8
[-1,-2,3,4]=>3
[-1,-2,3,-4]=>7
[-1,-2,-3,4]=>6
[-1,-2,-3,-4]=>10
[1,2,4,3]=>1
[1,2,4,-3]=>4
[1,2,-4,3]=>4
[1,2,-4,-3]=>6
[1,-2,4,3]=>3
[1,-2,4,-3]=>6
[1,-2,-4,3]=>6
[1,-2,-4,-3]=>8
[-1,2,4,3]=>2
[-1,2,4,-3]=>5
[-1,2,-4,3]=>5
[-1,2,-4,-3]=>7
[-1,-2,4,3]=>4
[-1,-2,4,-3]=>7
[-1,-2,-4,3]=>7
[-1,-2,-4,-3]=>9
[1,3,2,4]=>1
[1,3,2,-4]=>5
[1,3,-2,4]=>3
[1,3,-2,-4]=>7
[1,-3,2,4]=>3
[1,-3,2,-4]=>7
[1,-3,-2,4]=>4
[1,-3,-2,-4]=>8
[-1,3,2,4]=>2
[-1,3,2,-4]=>6
[-1,3,-2,4]=>4
[-1,3,-2,-4]=>8
[-1,-3,2,4]=>4
[-1,-3,2,-4]=>8
[-1,-3,-2,4]=>5
[-1,-3,-2,-4]=>9
[1,3,4,2]=>2
[1,3,4,-2]=>4
[1,3,-4,2]=>5
[1,3,-4,-2]=>6
[1,-3,4,2]=>4
[1,-3,4,-2]=>5
[1,-3,-4,2]=>6
[1,-3,-4,-2]=>8
[-1,3,4,2]=>3
[-1,3,4,-2]=>5
[-1,3,-4,2]=>6
[-1,3,-4,-2]=>7
[-1,-3,4,2]=>5
[-1,-3,4,-2]=>6
[-1,-3,-4,2]=>7
[-1,-3,-4,-2]=>9
[1,4,2,3]=>2
[1,4,2,-3]=>5
[1,4,-2,3]=>4
[1,4,-2,-3]=>6
[1,-4,2,3]=>4
[1,-4,2,-3]=>6
[1,-4,-2,3]=>5
[1,-4,-2,-3]=>8
[-1,4,2,3]=>3
[-1,4,2,-3]=>6
[-1,4,-2,3]=>5
[-1,4,-2,-3]=>7
[-1,-4,2,3]=>5
[-1,-4,2,-3]=>7
[-1,-4,-2,3]=>6
[-1,-4,-2,-3]=>9
[1,4,3,2]=>2
[1,4,3,-2]=>4
[1,4,-3,2]=>5
[1,4,-3,-2]=>6
[1,-4,3,2]=>4
[1,-4,3,-2]=>5
[1,-4,-3,2]=>6
[1,-4,-3,-2]=>8
[-1,4,3,2]=>3
[-1,4,3,-2]=>5
[-1,4,-3,2]=>6
[-1,4,-3,-2]=>7
[-1,-4,3,2]=>5
[-1,-4,3,-2]=>6
[-1,-4,-3,2]=>7
[-1,-4,-3,-2]=>9
[2,1,3,4]=>1
[2,1,3,-4]=>5
[2,1,-3,4]=>4
[2,1,-3,-4]=>8
[2,-1,3,4]=>2
[2,-1,3,-4]=>6
[2,-1,-3,4]=>5
[2,-1,-3,-4]=>9
[-2,1,3,4]=>2
[-2,1,3,-4]=>6
[-2,1,-3,4]=>5
[-2,1,-3,-4]=>9
[-2,-1,3,4]=>2
[-2,-1,3,-4]=>6
[-2,-1,-3,4]=>5
[-2,-1,-3,-4]=>9
[2,1,4,3]=>2
[2,1,4,-3]=>5
[2,1,-4,3]=>5
[2,1,-4,-3]=>7
[2,-1,4,3]=>3
[2,-1,4,-3]=>6
[2,-1,-4,3]=>6
[2,-1,-4,-3]=>8
[-2,1,4,3]=>3
[-2,1,4,-3]=>6
[-2,1,-4,3]=>6
[-2,1,-4,-3]=>8
[-2,-1,4,3]=>3
[-2,-1,4,-3]=>6
[-2,-1,-4,3]=>6
[-2,-1,-4,-3]=>8
[2,3,1,4]=>2
[2,3,1,-4]=>6
[2,3,-1,4]=>3
[2,3,-1,-4]=>7
[2,-3,1,4]=>4
[2,-3,1,-4]=>8
[2,-3,-1,4]=>4
[2,-3,-1,-4]=>8
[-2,3,1,4]=>3
[-2,3,1,-4]=>7
[-2,3,-1,4]=>3
[-2,3,-1,-4]=>7
[-2,-3,1,4]=>4
[-2,-3,1,-4]=>8
[-2,-3,-1,4]=>5
[-2,-3,-1,-4]=>9
[2,3,4,1]=>3
[2,3,4,-1]=>4
[2,3,-4,1]=>6
[2,3,-4,-1]=>6
[2,-3,4,1]=>5
[2,-3,4,-1]=>5
[2,-3,-4,1]=>7
[2,-3,-4,-1]=>8
[-2,3,4,1]=>4
[-2,3,4,-1]=>4
[-2,3,-4,1]=>6
[-2,3,-4,-1]=>7
[-2,-3,4,1]=>5
[-2,-3,4,-1]=>6
[-2,-3,-4,1]=>8
[-2,-3,-4,-1]=>8
[2,4,1,3]=>3
[2,4,1,-3]=>6
[2,4,-1,3]=>4
[2,4,-1,-3]=>6
[2,-4,1,3]=>5
[2,-4,1,-3]=>7
[2,-4,-1,3]=>5
[2,-4,-1,-3]=>8
[-2,4,1,3]=>4
[-2,4,1,-3]=>6
[-2,4,-1,3]=>4
[-2,4,-1,-3]=>7
[-2,-4,1,3]=>5
[-2,-4,1,-3]=>8
[-2,-4,-1,3]=>6
[-2,-4,-1,-3]=>8
[2,4,3,1]=>3
[2,4,3,-1]=>4
[2,4,-3,1]=>6
[2,4,-3,-1]=>6
[2,-4,3,1]=>5
[2,-4,3,-1]=>5
[2,-4,-3,1]=>7
[2,-4,-3,-1]=>8
[-2,4,3,1]=>4
[-2,4,3,-1]=>4
[-2,4,-3,1]=>6
[-2,4,-3,-1]=>7
[-2,-4,3,1]=>5
[-2,-4,3,-1]=>6
[-2,-4,-3,1]=>8
[-2,-4,-3,-1]=>8
[3,1,2,4]=>2
[3,1,2,-4]=>6
[3,1,-2,4]=>4
[3,1,-2,-4]=>8
[3,-1,2,4]=>3
[3,-1,2,-4]=>7
[3,-1,-2,4]=>4
[3,-1,-2,-4]=>8
[-3,1,2,4]=>3
[-3,1,2,-4]=>7
[-3,1,-2,4]=>4
[-3,1,-2,-4]=>8
[-3,-1,2,4]=>3
[-3,-1,2,-4]=>7
[-3,-1,-2,4]=>5
[-3,-1,-2,-4]=>9
[3,1,4,2]=>3
[3,1,4,-2]=>5
[3,1,-4,2]=>6
[3,1,-4,-2]=>7
[3,-1,4,2]=>4
[3,-1,4,-2]=>5
[3,-1,-4,2]=>6
[3,-1,-4,-2]=>8
[-3,1,4,2]=>4
[-3,1,4,-2]=>5
[-3,1,-4,2]=>6
[-3,1,-4,-2]=>8
[-3,-1,4,2]=>4
[-3,-1,4,-2]=>6
[-3,-1,-4,2]=>7
[-3,-1,-4,-2]=>8
[3,2,1,4]=>2
[3,2,1,-4]=>6
[3,2,-1,4]=>3
[3,2,-1,-4]=>7
[3,-2,1,4]=>4
[3,-2,1,-4]=>8
[3,-2,-1,4]=>4
[3,-2,-1,-4]=>8
[-3,2,1,4]=>3
[-3,2,1,-4]=>7
[-3,2,-1,4]=>3
[-3,2,-1,-4]=>7
[-3,-2,1,4]=>4
[-3,-2,1,-4]=>8
[-3,-2,-1,4]=>5
[-3,-2,-1,-4]=>9
[3,2,4,1]=>3
[3,2,4,-1]=>4
[3,2,-4,1]=>6
[3,2,-4,-1]=>6
[3,-2,4,1]=>5
[3,-2,4,-1]=>5
[3,-2,-4,1]=>7
[3,-2,-4,-1]=>8
[-3,2,4,1]=>4
[-3,2,4,-1]=>4
[-3,2,-4,1]=>6
[-3,2,-4,-1]=>7
[-3,-2,4,1]=>5
[-3,-2,4,-1]=>6
[-3,-2,-4,1]=>8
[-3,-2,-4,-1]=>8
[3,4,1,2]=>4
[3,4,1,-2]=>6
[3,4,-1,2]=>5
[3,4,-1,-2]=>6
[3,-4,1,2]=>6
[3,-4,1,-2]=>7
[3,-4,-1,2]=>6
[3,-4,-1,-2]=>8
[-3,4,1,2]=>5
[-3,4,1,-2]=>6
[-3,4,-1,2]=>5
[-3,4,-1,-2]=>7
[-3,-4,1,2]=>6
[-3,-4,1,-2]=>8
[-3,-4,-1,2]=>7
[-3,-4,-1,-2]=>8
[3,4,2,1]=>4
[3,4,2,-1]=>5
[3,4,-2,1]=>6
[3,4,-2,-1]=>6
[3,-4,2,1]=>6
[3,-4,2,-1]=>6
[3,-4,-2,1]=>7
[3,-4,-2,-1]=>8
[-3,4,2,1]=>5
[-3,4,2,-1]=>5
[-3,4,-2,1]=>6
[-3,4,-2,-1]=>7
[-3,-4,2,1]=>6
[-3,-4,2,-1]=>7
[-3,-4,-2,1]=>8
[-3,-4,-2,-1]=>8
[4,1,2,3]=>3
[4,1,2,-3]=>6
[4,1,-2,3]=>5
[4,1,-2,-3]=>7
[4,-1,2,3]=>4
[4,-1,2,-3]=>6
[4,-1,-2,3]=>5
[4,-1,-2,-3]=>8
[-4,1,2,3]=>4
[-4,1,2,-3]=>6
[-4,1,-2,3]=>5
[-4,1,-2,-3]=>8
[-4,-1,2,3]=>4
[-4,-1,2,-3]=>7
[-4,-1,-2,3]=>6
[-4,-1,-2,-3]=>8
[4,1,3,2]=>3
[4,1,3,-2]=>5
[4,1,-3,2]=>6
[4,1,-3,-2]=>7
[4,-1,3,2]=>4
[4,-1,3,-2]=>5
[4,-1,-3,2]=>6
[4,-1,-3,-2]=>8
[-4,1,3,2]=>4
[-4,1,3,-2]=>5
[-4,1,-3,2]=>6
[-4,1,-3,-2]=>8
[-4,-1,3,2]=>4
[-4,-1,3,-2]=>6
[-4,-1,-3,2]=>7
[-4,-1,-3,-2]=>8
[4,2,1,3]=>3
[4,2,1,-3]=>6
[4,2,-1,3]=>4
[4,2,-1,-3]=>6
[4,-2,1,3]=>5
[4,-2,1,-3]=>7
[4,-2,-1,3]=>5
[4,-2,-1,-3]=>8
[-4,2,1,3]=>4
[-4,2,1,-3]=>6
[-4,2,-1,3]=>4
[-4,2,-1,-3]=>7
[-4,-2,1,3]=>5
[-4,-2,1,-3]=>8
[-4,-2,-1,3]=>6
[-4,-2,-1,-3]=>8
[4,2,3,1]=>3
[4,2,3,-1]=>4
[4,2,-3,1]=>6
[4,2,-3,-1]=>6
[4,-2,3,1]=>5
[4,-2,3,-1]=>5
[4,-2,-3,1]=>7
[4,-2,-3,-1]=>8
[-4,2,3,1]=>4
[-4,2,3,-1]=>4
[-4,2,-3,1]=>6
[-4,2,-3,-1]=>7
[-4,-2,3,1]=>5
[-4,-2,3,-1]=>6
[-4,-2,-3,1]=>8
[-4,-2,-3,-1]=>8
[4,3,1,2]=>4
[4,3,1,-2]=>6
[4,3,-1,2]=>5
[4,3,-1,-2]=>6
[4,-3,1,2]=>6
[4,-3,1,-2]=>7
[4,-3,-1,2]=>6
[4,-3,-1,-2]=>8
[-4,3,1,2]=>5
[-4,3,1,-2]=>6
[-4,3,-1,2]=>5
[-4,3,-1,-2]=>7
[-4,-3,1,2]=>6
[-4,-3,1,-2]=>8
[-4,-3,-1,2]=>7
[-4,-3,-1,-2]=>8
[4,3,2,1]=>4
[4,3,2,-1]=>5
[4,3,-2,1]=>6
[4,3,-2,-1]=>6
[4,-3,2,1]=>6
[4,-3,2,-1]=>6
[4,-3,-2,1]=>7
[4,-3,-2,-1]=>8
[-4,3,2,1]=>5
[-4,3,2,-1]=>5
[-4,3,-2,1]=>6
[-4,3,-2,-1]=>7
[-4,-3,2,1]=>6
[-4,-3,2,-1]=>7
[-4,-3,-2,1]=>8
[-4,-3,-2,-1]=>8
[1,2,3,4,5]=>0
[1,2,3,4,-5]=>5
[1,2,3,-4,5]=>4
[1,2,3,-4,-5]=>9
[1,2,-3,4,5]=>3
[1,2,-3,4,-5]=>8
[1,2,-3,-4,5]=>7
[1,2,-3,-4,-5]=>12
[1,-2,3,4,5]=>2
[1,-2,3,4,-5]=>7
[1,-2,3,-4,5]=>6
[1,-2,3,-4,-5]=>11
[1,-2,-3,4,5]=>5
[1,-2,-3,4,-5]=>10
[1,-2,-3,-4,5]=>9
[1,-2,-3,-4,-5]=>14
[-1,2,3,4,5]=>1
[-1,2,3,4,-5]=>6
[-1,2,3,-4,5]=>5
[-1,2,3,-4,-5]=>10
[-1,2,-3,4,5]=>4
[-1,2,-3,4,-5]=>9
[-1,2,-3,-4,5]=>8
[-1,2,-3,-4,-5]=>13
[-1,-2,3,4,5]=>3
[-1,-2,3,4,-5]=>8
[-1,-2,3,-4,5]=>7
[-1,-2,3,-4,-5]=>12
[-1,-2,-3,4,5]=>6
[-1,-2,-3,4,-5]=>11
[-1,-2,-3,-4,5]=>10
[-1,-2,-3,-4,-5]=>15
[1,2,3,5,4]=>1
[1,2,3,5,-4]=>5
[1,2,3,-5,4]=>5
[1,2,3,-5,-4]=>8
[1,2,-3,5,4]=>4
[1,2,-3,5,-4]=>8
[1,2,-3,-5,4]=>8
[1,2,-3,-5,-4]=>11
[1,-2,3,5,4]=>3
[1,-2,3,5,-4]=>7
[1,-2,3,-5,4]=>7
[1,-2,3,-5,-4]=>10
[1,-2,-3,5,4]=>6
[1,-2,-3,5,-4]=>10
[1,-2,-3,-5,4]=>10
[1,-2,-3,-5,-4]=>13
[-1,2,3,5,4]=>2
[-1,2,3,5,-4]=>6
[-1,2,3,-5,4]=>6
[-1,2,3,-5,-4]=>9
[-1,2,-3,5,4]=>5
[-1,2,-3,5,-4]=>9
[-1,2,-3,-5,4]=>9
[-1,2,-3,-5,-4]=>12
[-1,-2,3,5,4]=>4
[-1,-2,3,5,-4]=>8
[-1,-2,3,-5,4]=>8
[-1,-2,3,-5,-4]=>11
[-1,-2,-3,5,4]=>7
[-1,-2,-3,5,-4]=>11
[-1,-2,-3,-5,4]=>11
[-1,-2,-3,-5,-4]=>14
[1,2,4,3,5]=>1
[1,2,4,3,-5]=>6
[1,2,4,-3,5]=>4
[1,2,4,-3,-5]=>9
[1,2,-4,3,5]=>4
[1,2,-4,3,-5]=>9
[1,2,-4,-3,5]=>6
[1,2,-4,-3,-5]=>11
[1,-2,4,3,5]=>3
[1,-2,4,3,-5]=>8
[1,-2,4,-3,5]=>6
[1,-2,4,-3,-5]=>11
[1,-2,-4,3,5]=>6
[1,-2,-4,3,-5]=>11
[1,-2,-4,-3,5]=>8
[1,-2,-4,-3,-5]=>13
[-1,2,4,3,5]=>2
[-1,2,4,3,-5]=>7
[-1,2,4,-3,5]=>5
[-1,2,4,-3,-5]=>10
[-1,2,-4,3,5]=>5
[-1,2,-4,3,-5]=>10
[-1,2,-4,-3,5]=>7
[-1,2,-4,-3,-5]=>12
[-1,-2,4,3,5]=>4
[-1,-2,4,3,-5]=>9
[-1,-2,4,-3,5]=>7
[-1,-2,4,-3,-5]=>12
[-1,-2,-4,3,5]=>7
[-1,-2,-4,3,-5]=>12
[-1,-2,-4,-3,5]=>9
[-1,-2,-4,-3,-5]=>14
[1,2,4,5,3]=>2
[1,2,4,5,-3]=>5
[1,2,4,-5,3]=>6
[1,2,4,-5,-3]=>8
[1,2,-4,5,3]=>5
[1,2,-4,5,-3]=>7
[1,2,-4,-5,3]=>8
[1,2,-4,-5,-3]=>11
[1,-2,4,5,3]=>4
[1,-2,4,5,-3]=>7
[1,-2,4,-5,3]=>8
[1,-2,4,-5,-3]=>10
[1,-2,-4,5,3]=>7
[1,-2,-4,5,-3]=>9
[1,-2,-4,-5,3]=>10
[1,-2,-4,-5,-3]=>13
[-1,2,4,5,3]=>3
[-1,2,4,5,-3]=>6
[-1,2,4,-5,3]=>7
[-1,2,4,-5,-3]=>9
[-1,2,-4,5,3]=>6
[-1,2,-4,5,-3]=>8
[-1,2,-4,-5,3]=>9
[-1,2,-4,-5,-3]=>12
[-1,-2,4,5,3]=>5
[-1,-2,4,5,-3]=>8
[-1,-2,4,-5,3]=>9
[-1,-2,4,-5,-3]=>11
[-1,-2,-4,5,3]=>8
[-1,-2,-4,5,-3]=>10
[-1,-2,-4,-5,3]=>11
[-1,-2,-4,-5,-3]=>14
[1,2,5,3,4]=>2
[1,2,5,3,-4]=>6
[1,2,5,-3,4]=>5
[1,2,5,-3,-4]=>8
[1,2,-5,3,4]=>5
[1,2,-5,3,-4]=>8
[1,2,-5,-3,4]=>7
[1,2,-5,-3,-4]=>11
[1,-2,5,3,4]=>4
[1,-2,5,3,-4]=>8
[1,-2,5,-3,4]=>7
[1,-2,5,-3,-4]=>10
[1,-2,-5,3,4]=>7
[1,-2,-5,3,-4]=>10
[1,-2,-5,-3,4]=>9
[1,-2,-5,-3,-4]=>13
[-1,2,5,3,4]=>3
[-1,2,5,3,-4]=>7
[-1,2,5,-3,4]=>6
[-1,2,5,-3,-4]=>9
[-1,2,-5,3,4]=>6
[-1,2,-5,3,-4]=>9
[-1,2,-5,-3,4]=>8
[-1,2,-5,-3,-4]=>12
[-1,-2,5,3,4]=>5
[-1,-2,5,3,-4]=>9
[-1,-2,5,-3,4]=>8
[-1,-2,5,-3,-4]=>11
[-1,-2,-5,3,4]=>8
[-1,-2,-5,3,-4]=>11
[-1,-2,-5,-3,4]=>10
[-1,-2,-5,-3,-4]=>14
[1,2,5,4,3]=>2
[1,2,5,4,-3]=>5
[1,2,5,-4,3]=>6
[1,2,5,-4,-3]=>8
[1,2,-5,4,3]=>5
[1,2,-5,4,-3]=>7
[1,2,-5,-4,3]=>8
[1,2,-5,-4,-3]=>11
[1,-2,5,4,3]=>4
[1,-2,5,4,-3]=>7
[1,-2,5,-4,3]=>8
[1,-2,5,-4,-3]=>10
[1,-2,-5,4,3]=>7
[1,-2,-5,4,-3]=>9
[1,-2,-5,-4,3]=>10
[1,-2,-5,-4,-3]=>13
[-1,2,5,4,3]=>3
[-1,2,5,4,-3]=>6
[-1,2,5,-4,3]=>7
[-1,2,5,-4,-3]=>9
[-1,2,-5,4,3]=>6
[-1,2,-5,4,-3]=>8
[-1,2,-5,-4,3]=>9
[-1,2,-5,-4,-3]=>12
[-1,-2,5,4,3]=>5
[-1,-2,5,4,-3]=>8
[-1,-2,5,-4,3]=>9
[-1,-2,5,-4,-3]=>11
[-1,-2,-5,4,3]=>8
[-1,-2,-5,4,-3]=>10
[-1,-2,-5,-4,3]=>11
[-1,-2,-5,-4,-3]=>14
[1,3,2,4,5]=>1
[1,3,2,4,-5]=>6
[1,3,2,-4,5]=>5
[1,3,2,-4,-5]=>10
[1,3,-2,4,5]=>3
[1,3,-2,4,-5]=>8
[1,3,-2,-4,5]=>7
[1,3,-2,-4,-5]=>12
[1,-3,2,4,5]=>3
[1,-3,2,4,-5]=>8
[1,-3,2,-4,5]=>7
[1,-3,2,-4,-5]=>12
[1,-3,-2,4,5]=>4
[1,-3,-2,4,-5]=>9
[1,-3,-2,-4,5]=>8
[1,-3,-2,-4,-5]=>13
[-1,3,2,4,5]=>2
[-1,3,2,4,-5]=>7
[-1,3,2,-4,5]=>6
[-1,3,2,-4,-5]=>11
[-1,3,-2,4,5]=>4
[-1,3,-2,4,-5]=>9
[-1,3,-2,-4,5]=>8
[-1,3,-2,-4,-5]=>13
[-1,-3,2,4,5]=>4
[-1,-3,2,4,-5]=>9
[-1,-3,2,-4,5]=>8
[-1,-3,2,-4,-5]=>13
[-1,-3,-2,4,5]=>5
[-1,-3,-2,4,-5]=>10
[-1,-3,-2,-4,5]=>9
[-1,-3,-2,-4,-5]=>14
[1,3,2,5,4]=>2
[1,3,2,5,-4]=>6
[1,3,2,-5,4]=>6
[1,3,2,-5,-4]=>9
[1,3,-2,5,4]=>4
[1,3,-2,5,-4]=>8
[1,3,-2,-5,4]=>8
[1,3,-2,-5,-4]=>11
[1,-3,2,5,4]=>4
[1,-3,2,5,-4]=>8
[1,-3,2,-5,4]=>8
[1,-3,2,-5,-4]=>11
[1,-3,-2,5,4]=>5
[1,-3,-2,5,-4]=>9
[1,-3,-2,-5,4]=>9
[1,-3,-2,-5,-4]=>12
[-1,3,2,5,4]=>3
[-1,3,2,5,-4]=>7
[-1,3,2,-5,4]=>7
[-1,3,2,-5,-4]=>10
[-1,3,-2,5,4]=>5
[-1,3,-2,5,-4]=>9
[-1,3,-2,-5,4]=>9
[-1,3,-2,-5,-4]=>12
[-1,-3,2,5,4]=>5
[-1,-3,2,5,-4]=>9
[-1,-3,2,-5,4]=>9
[-1,-3,2,-5,-4]=>12
[-1,-3,-2,5,4]=>6
[-1,-3,-2,5,-4]=>10
[-1,-3,-2,-5,4]=>10
[-1,-3,-2,-5,-4]=>13
[1,3,4,2,5]=>2
[1,3,4,2,-5]=>7
[1,3,4,-2,5]=>4
[1,3,4,-2,-5]=>9
[1,3,-4,2,5]=>5
[1,3,-4,2,-5]=>10
[1,3,-4,-2,5]=>6
[1,3,-4,-2,-5]=>11
[1,-3,4,2,5]=>4
[1,-3,4,2,-5]=>9
[1,-3,4,-2,5]=>5
[1,-3,4,-2,-5]=>10
[1,-3,-4,2,5]=>6
[1,-3,-4,2,-5]=>11
[1,-3,-4,-2,5]=>8
[1,-3,-4,-2,-5]=>13
[-1,3,4,2,5]=>3
[-1,3,4,2,-5]=>8
[-1,3,4,-2,5]=>5
[-1,3,4,-2,-5]=>10
[-1,3,-4,2,5]=>6
[-1,3,-4,2,-5]=>11
[-1,3,-4,-2,5]=>7
[-1,3,-4,-2,-5]=>12
[-1,-3,4,2,5]=>5
[-1,-3,4,2,-5]=>10
[-1,-3,4,-2,5]=>6
[-1,-3,4,-2,-5]=>11
[-1,-3,-4,2,5]=>7
[-1,-3,-4,2,-5]=>12
[-1,-3,-4,-2,5]=>9
[-1,-3,-4,-2,-5]=>14
[1,3,4,5,2]=>3
[1,3,4,5,-2]=>5
[1,3,4,-5,2]=>7
[1,3,4,-5,-2]=>8
[1,3,-4,5,2]=>6
[1,3,-4,5,-2]=>7
[1,3,-4,-5,2]=>9
[1,3,-4,-5,-2]=>11
[1,-3,4,5,2]=>5
[1,-3,4,5,-2]=>6
[1,-3,4,-5,2]=>8
[1,-3,4,-5,-2]=>10
[1,-3,-4,5,2]=>7
[1,-3,-4,5,-2]=>9
[1,-3,-4,-5,2]=>11
[1,-3,-4,-5,-2]=>12
[-1,3,4,5,2]=>4
[-1,3,4,5,-2]=>6
[-1,3,4,-5,2]=>8
[-1,3,4,-5,-2]=>9
[-1,3,-4,5,2]=>7
[-1,3,-4,5,-2]=>8
[-1,3,-4,-5,2]=>10
[-1,3,-4,-5,-2]=>12
[-1,-3,4,5,2]=>6
[-1,-3,4,5,-2]=>7
[-1,-3,4,-5,2]=>9
[-1,-3,4,-5,-2]=>11
[-1,-3,-4,5,2]=>8
[-1,-3,-4,5,-2]=>10
[-1,-3,-4,-5,2]=>12
[-1,-3,-4,-5,-2]=>13
[1,3,5,2,4]=>3
[1,3,5,2,-4]=>7
[1,3,5,-2,4]=>5
[1,3,5,-2,-4]=>8
[1,3,-5,2,4]=>6
[1,3,-5,2,-4]=>9
[1,3,-5,-2,4]=>7
[1,3,-5,-2,-4]=>11
[1,-3,5,2,4]=>5
[1,-3,5,2,-4]=>8
[1,-3,5,-2,4]=>6
[1,-3,5,-2,-4]=>10
[1,-3,-5,2,4]=>7
[1,-3,-5,2,-4]=>11
[1,-3,-5,-2,4]=>9
[1,-3,-5,-2,-4]=>12
[-1,3,5,2,4]=>4
[-1,3,5,2,-4]=>8
[-1,3,5,-2,4]=>6
[-1,3,5,-2,-4]=>9
[-1,3,-5,2,4]=>7
[-1,3,-5,2,-4]=>10
[-1,3,-5,-2,4]=>8
[-1,3,-5,-2,-4]=>12
[-1,-3,5,2,4]=>6
[-1,-3,5,2,-4]=>9
[-1,-3,5,-2,4]=>7
[-1,-3,5,-2,-4]=>11
[-1,-3,-5,2,4]=>8
[-1,-3,-5,2,-4]=>12
[-1,-3,-5,-2,4]=>10
[-1,-3,-5,-2,-4]=>13
[1,3,5,4,2]=>3
[1,3,5,4,-2]=>5
[1,3,5,-4,2]=>7
[1,3,5,-4,-2]=>8
[1,3,-5,4,2]=>6
[1,3,-5,4,-2]=>7
[1,3,-5,-4,2]=>9
[1,3,-5,-4,-2]=>11
[1,-3,5,4,2]=>5
[1,-3,5,4,-2]=>6
[1,-3,5,-4,2]=>8
[1,-3,5,-4,-2]=>10
[1,-3,-5,4,2]=>7
[1,-3,-5,4,-2]=>9
[1,-3,-5,-4,2]=>11
[1,-3,-5,-4,-2]=>12
[-1,3,5,4,2]=>4
[-1,3,5,4,-2]=>6
[-1,3,5,-4,2]=>8
[-1,3,5,-4,-2]=>9
[-1,3,-5,4,2]=>7
[-1,3,-5,4,-2]=>8
[-1,3,-5,-4,2]=>10
[-1,3,-5,-4,-2]=>12
[-1,-3,5,4,2]=>6
[-1,-3,5,4,-2]=>7
[-1,-3,5,-4,2]=>9
[-1,-3,5,-4,-2]=>11
[-1,-3,-5,4,2]=>8
[-1,-3,-5,4,-2]=>10
[-1,-3,-5,-4,2]=>12
[-1,-3,-5,-4,-2]=>13
[1,4,2,3,5]=>2
[1,4,2,3,-5]=>7
[1,4,2,-3,5]=>5
[1,4,2,-3,-5]=>10
[1,4,-2,3,5]=>4
[1,4,-2,3,-5]=>9
[1,4,-2,-3,5]=>6
[1,4,-2,-3,-5]=>11
[1,-4,2,3,5]=>4
[1,-4,2,3,-5]=>9
[1,-4,2,-3,5]=>6
[1,-4,2,-3,-5]=>11
[1,-4,-2,3,5]=>5
[1,-4,-2,3,-5]=>10
[1,-4,-2,-3,5]=>8
[1,-4,-2,-3,-5]=>13
[-1,4,2,3,5]=>3
[-1,4,2,3,-5]=>8
[-1,4,2,-3,5]=>6
[-1,4,2,-3,-5]=>11
[-1,4,-2,3,5]=>5
[-1,4,-2,3,-5]=>10
[-1,4,-2,-3,5]=>7
[-1,4,-2,-3,-5]=>12
[-1,-4,2,3,5]=>5
[-1,-4,2,3,-5]=>10
[-1,-4,2,-3,5]=>7
[-1,-4,2,-3,-5]=>12
[-1,-4,-2,3,5]=>6
[-1,-4,-2,3,-5]=>11
[-1,-4,-2,-3,5]=>9
[-1,-4,-2,-3,-5]=>14
[1,4,2,5,3]=>3
[1,4,2,5,-3]=>6
[1,4,2,-5,3]=>7
[1,4,2,-5,-3]=>9
[1,4,-2,5,3]=>5
[1,4,-2,5,-3]=>7
[1,4,-2,-5,3]=>8
[1,4,-2,-5,-3]=>11
[1,-4,2,5,3]=>5
[1,-4,2,5,-3]=>7
[1,-4,2,-5,3]=>8
[1,-4,2,-5,-3]=>11
[1,-4,-2,5,3]=>6
[1,-4,-2,5,-3]=>9
[1,-4,-2,-5,3]=>10
[1,-4,-2,-5,-3]=>12
[-1,4,2,5,3]=>4
[-1,4,2,5,-3]=>7
[-1,4,2,-5,3]=>8
[-1,4,2,-5,-3]=>10
[-1,4,-2,5,3]=>6
[-1,4,-2,5,-3]=>8
[-1,4,-2,-5,3]=>9
[-1,4,-2,-5,-3]=>12
[-1,-4,2,5,3]=>6
[-1,-4,2,5,-3]=>8
[-1,-4,2,-5,3]=>9
[-1,-4,2,-5,-3]=>12
[-1,-4,-2,5,3]=>7
[-1,-4,-2,5,-3]=>10
[-1,-4,-2,-5,3]=>11
[-1,-4,-2,-5,-3]=>13
[1,4,3,2,5]=>2
[1,4,3,2,-5]=>7
[1,4,3,-2,5]=>4
[1,4,3,-2,-5]=>9
[1,4,-3,2,5]=>5
[1,4,-3,2,-5]=>10
[1,4,-3,-2,5]=>6
[1,4,-3,-2,-5]=>11
[1,-4,3,2,5]=>4
[1,-4,3,2,-5]=>9
[1,-4,3,-2,5]=>5
[1,-4,3,-2,-5]=>10
[1,-4,-3,2,5]=>6
[1,-4,-3,2,-5]=>11
[1,-4,-3,-2,5]=>8
[1,-4,-3,-2,-5]=>13
[-1,4,3,2,5]=>3
[-1,4,3,2,-5]=>8
[-1,4,3,-2,5]=>5
[-1,4,3,-2,-5]=>10
[-1,4,-3,2,5]=>6
[-1,4,-3,2,-5]=>11
[-1,4,-3,-2,5]=>7
[-1,4,-3,-2,-5]=>12
[-1,-4,3,2,5]=>5
[-1,-4,3,2,-5]=>10
[-1,-4,3,-2,5]=>6
[-1,-4,3,-2,-5]=>11
[-1,-4,-3,2,5]=>7
[-1,-4,-3,2,-5]=>12
[-1,-4,-3,-2,5]=>9
[-1,-4,-3,-2,-5]=>14
[1,4,3,5,2]=>3
[1,4,3,5,-2]=>5
[1,4,3,-5,2]=>7
[1,4,3,-5,-2]=>8
[1,4,-3,5,2]=>6
[1,4,-3,5,-2]=>7
[1,4,-3,-5,2]=>9
[1,4,-3,-5,-2]=>11
[1,-4,3,5,2]=>5
[1,-4,3,5,-2]=>6
[1,-4,3,-5,2]=>8
[1,-4,3,-5,-2]=>10
[1,-4,-3,5,2]=>7
[1,-4,-3,5,-2]=>9
[1,-4,-3,-5,2]=>11
[1,-4,-3,-5,-2]=>12
[-1,4,3,5,2]=>4
[-1,4,3,5,-2]=>6
[-1,4,3,-5,2]=>8
[-1,4,3,-5,-2]=>9
[-1,4,-3,5,2]=>7
[-1,4,-3,5,-2]=>8
[-1,4,-3,-5,2]=>10
[-1,4,-3,-5,-2]=>12
[-1,-4,3,5,2]=>6
[-1,-4,3,5,-2]=>7
[-1,-4,3,-5,2]=>9
[-1,-4,3,-5,-2]=>11
[-1,-4,-3,5,2]=>8
[-1,-4,-3,5,-2]=>10
[-1,-4,-3,-5,2]=>12
[-1,-4,-3,-5,-2]=>13
[1,4,5,2,3]=>4
[1,4,5,2,-3]=>7
[1,4,5,-2,3]=>6
[1,4,5,-2,-3]=>8
[1,4,-5,2,3]=>7
[1,4,-5,2,-3]=>9
[1,4,-5,-2,3]=>8
[1,4,-5,-2,-3]=>11
[1,-4,5,2,3]=>6
[1,-4,5,2,-3]=>8
[1,-4,5,-2,3]=>7
[1,-4,5,-2,-3]=>10
[1,-4,-5,2,3]=>8
[1,-4,-5,2,-3]=>11
[1,-4,-5,-2,3]=>10
[1,-4,-5,-2,-3]=>12
[-1,4,5,2,3]=>5
[-1,4,5,2,-3]=>8
[-1,4,5,-2,3]=>7
[-1,4,5,-2,-3]=>9
[-1,4,-5,2,3]=>8
[-1,4,-5,2,-3]=>10
[-1,4,-5,-2,3]=>9
[-1,4,-5,-2,-3]=>12
[-1,-4,5,2,3]=>7
[-1,-4,5,2,-3]=>9
[-1,-4,5,-2,3]=>8
[-1,-4,5,-2,-3]=>11
[-1,-4,-5,2,3]=>9
[-1,-4,-5,2,-3]=>12
[-1,-4,-5,-2,3]=>11
[-1,-4,-5,-2,-3]=>13
[1,4,5,3,2]=>4
[1,4,5,3,-2]=>6
[1,4,5,-3,2]=>7
[1,4,5,-3,-2]=>8
[1,4,-5,3,2]=>7
[1,4,-5,3,-2]=>8
[1,4,-5,-3,2]=>9
[1,4,-5,-3,-2]=>11
[1,-4,5,3,2]=>6
[1,-4,5,3,-2]=>7
[1,-4,5,-3,2]=>8
[1,-4,5,-3,-2]=>10
[1,-4,-5,3,2]=>8
[1,-4,-5,3,-2]=>10
[1,-4,-5,-3,2]=>11
[1,-4,-5,-3,-2]=>12
[-1,4,5,3,2]=>5
[-1,4,5,3,-2]=>7
[-1,4,5,-3,2]=>8
[-1,4,5,-3,-2]=>9
[-1,4,-5,3,2]=>8
[-1,4,-5,3,-2]=>9
[-1,4,-5,-3,2]=>10
[-1,4,-5,-3,-2]=>12
[-1,-4,5,3,2]=>7
[-1,-4,5,3,-2]=>8
[-1,-4,5,-3,2]=>9
[-1,-4,5,-3,-2]=>11
[-1,-4,-5,3,2]=>9
[-1,-4,-5,3,-2]=>11
[-1,-4,-5,-3,2]=>12
[-1,-4,-5,-3,-2]=>13
[1,5,2,3,4]=>3
[1,5,2,3,-4]=>7
[1,5,2,-3,4]=>6
[1,5,2,-3,-4]=>9
[1,5,-2,3,4]=>5
[1,5,-2,3,-4]=>8
[1,5,-2,-3,4]=>7
[1,5,-2,-3,-4]=>11
[1,-5,2,3,4]=>5
[1,-5,2,3,-4]=>8
[1,-5,2,-3,4]=>7
[1,-5,2,-3,-4]=>11
[1,-5,-2,3,4]=>6
[1,-5,-2,3,-4]=>10
[1,-5,-2,-3,4]=>9
[1,-5,-2,-3,-4]=>12
[-1,5,2,3,4]=>4
[-1,5,2,3,-4]=>8
[-1,5,2,-3,4]=>7
[-1,5,2,-3,-4]=>10
[-1,5,-2,3,4]=>6
[-1,5,-2,3,-4]=>9
[-1,5,-2,-3,4]=>8
[-1,5,-2,-3,-4]=>12
[-1,-5,2,3,4]=>6
[-1,-5,2,3,-4]=>9
[-1,-5,2,-3,4]=>8
[-1,-5,2,-3,-4]=>12
[-1,-5,-2,3,4]=>7
[-1,-5,-2,3,-4]=>11
[-1,-5,-2,-3,4]=>10
[-1,-5,-2,-3,-4]=>13
[1,5,2,4,3]=>3
[1,5,2,4,-3]=>6
[1,5,2,-4,3]=>7
[1,5,2,-4,-3]=>9
[1,5,-2,4,3]=>5
[1,5,-2,4,-3]=>7
[1,5,-2,-4,3]=>8
[1,5,-2,-4,-3]=>11
[1,-5,2,4,3]=>5
[1,-5,2,4,-3]=>7
[1,-5,2,-4,3]=>8
[1,-5,2,-4,-3]=>11
[1,-5,-2,4,3]=>6
[1,-5,-2,4,-3]=>9
[1,-5,-2,-4,3]=>10
[1,-5,-2,-4,-3]=>12
[-1,5,2,4,3]=>4
[-1,5,2,4,-3]=>7
[-1,5,2,-4,3]=>8
[-1,5,2,-4,-3]=>10
[-1,5,-2,4,3]=>6
[-1,5,-2,4,-3]=>8
[-1,5,-2,-4,3]=>9
[-1,5,-2,-4,-3]=>12
[-1,-5,2,4,3]=>6
[-1,-5,2,4,-3]=>8
[-1,-5,2,-4,3]=>9
[-1,-5,2,-4,-3]=>12
[-1,-5,-2,4,3]=>7
[-1,-5,-2,4,-3]=>10
[-1,-5,-2,-4,3]=>11
[-1,-5,-2,-4,-3]=>13
[1,5,3,2,4]=>3
[1,5,3,2,-4]=>7
[1,5,3,-2,4]=>5
[1,5,3,-2,-4]=>8
[1,5,-3,2,4]=>6
[1,5,-3,2,-4]=>9
[1,5,-3,-2,4]=>7
[1,5,-3,-2,-4]=>11
[1,-5,3,2,4]=>5
[1,-5,3,2,-4]=>8
[1,-5,3,-2,4]=>6
[1,-5,3,-2,-4]=>10
[1,-5,-3,2,4]=>7
[1,-5,-3,2,-4]=>11
[1,-5,-3,-2,4]=>9
[1,-5,-3,-2,-4]=>12
[-1,5,3,2,4]=>4
[-1,5,3,2,-4]=>8
[-1,5,3,-2,4]=>6
[-1,5,3,-2,-4]=>9
[-1,5,-3,2,4]=>7
[-1,5,-3,2,-4]=>10
[-1,5,-3,-2,4]=>8
[-1,5,-3,-2,-4]=>12
[-1,-5,3,2,4]=>6
[-1,-5,3,2,-4]=>9
[-1,-5,3,-2,4]=>7
[-1,-5,3,-2,-4]=>11
[-1,-5,-3,2,4]=>8
[-1,-5,-3,2,-4]=>12
[-1,-5,-3,-2,4]=>10
[-1,-5,-3,-2,-4]=>13
[1,5,3,4,2]=>3
[1,5,3,4,-2]=>5
[1,5,3,-4,2]=>7
[1,5,3,-4,-2]=>8
[1,5,-3,4,2]=>6
[1,5,-3,4,-2]=>7
[1,5,-3,-4,2]=>9
[1,5,-3,-4,-2]=>11
[1,-5,3,4,2]=>5
[1,-5,3,4,-2]=>6
[1,-5,3,-4,2]=>8
[1,-5,3,-4,-2]=>10
[1,-5,-3,4,2]=>7
[1,-5,-3,4,-2]=>9
[1,-5,-3,-4,2]=>11
[1,-5,-3,-4,-2]=>12
[-1,5,3,4,2]=>4
[-1,5,3,4,-2]=>6
[-1,5,3,-4,2]=>8
[-1,5,3,-4,-2]=>9
[-1,5,-3,4,2]=>7
[-1,5,-3,4,-2]=>8
[-1,5,-3,-4,2]=>10
[-1,5,-3,-4,-2]=>12
[-1,-5,3,4,2]=>6
[-1,-5,3,4,-2]=>7
[-1,-5,3,-4,2]=>9
[-1,-5,3,-4,-2]=>11
[-1,-5,-3,4,2]=>8
[-1,-5,-3,4,-2]=>10
[-1,-5,-3,-4,2]=>12
[-1,-5,-3,-4,-2]=>13
[1,5,4,2,3]=>4
[1,5,4,2,-3]=>7
[1,5,4,-2,3]=>6
[1,5,4,-2,-3]=>8
[1,5,-4,2,3]=>7
[1,5,-4,2,-3]=>9
[1,5,-4,-2,3]=>8
[1,5,-4,-2,-3]=>11
[1,-5,4,2,3]=>6
[1,-5,4,2,-3]=>8
[1,-5,4,-2,3]=>7
[1,-5,4,-2,-3]=>10
[1,-5,-4,2,3]=>8
[1,-5,-4,2,-3]=>11
[1,-5,-4,-2,3]=>10
[1,-5,-4,-2,-3]=>12
[-1,5,4,2,3]=>5
[-1,5,4,2,-3]=>8
[-1,5,4,-2,3]=>7
[-1,5,4,-2,-3]=>9
[-1,5,-4,2,3]=>8
[-1,5,-4,2,-3]=>10
[-1,5,-4,-2,3]=>9
[-1,5,-4,-2,-3]=>12
[-1,-5,4,2,3]=>7
[-1,-5,4,2,-3]=>9
[-1,-5,4,-2,3]=>8
[-1,-5,4,-2,-3]=>11
[-1,-5,-4,2,3]=>9
[-1,-5,-4,2,-3]=>12
[-1,-5,-4,-2,3]=>11
[-1,-5,-4,-2,-3]=>13
[1,5,4,3,2]=>4
[1,5,4,3,-2]=>6
[1,5,4,-3,2]=>7
[1,5,4,-3,-2]=>8
[1,5,-4,3,2]=>7
[1,5,-4,3,-2]=>8
[1,5,-4,-3,2]=>9
[1,5,-4,-3,-2]=>11
[1,-5,4,3,2]=>6
[1,-5,4,3,-2]=>7
[1,-5,4,-3,2]=>8
[1,-5,4,-3,-2]=>10
[1,-5,-4,3,2]=>8
[1,-5,-4,3,-2]=>10
[1,-5,-4,-3,2]=>11
[1,-5,-4,-3,-2]=>12
[-1,5,4,3,2]=>5
[-1,5,4,3,-2]=>7
[-1,5,4,-3,2]=>8
[-1,5,4,-3,-2]=>9
[-1,5,-4,3,2]=>8
[-1,5,-4,3,-2]=>9
                    

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Description

The depth of a signed permutation.
The depth of a positive root is its rank in the root poset. The depth of an element of a Coxeter group is the minimal sum of depths for any representation as product of reflections.

References

[1] Petersen, T. K., Tenner, B. E. The depth of a permutation arXiv:1202.4765
[2] Bagno, E., Biagioli, R., Novick, M., Woo, A. Depth in classical Coexter groups arXiv:1507.01180

Code

def statistic(sigma):
    """
    sage: sigma = SignedPermutation([2,-4,3,-1,7,-5,6])
    sage: statistic(sigma)
    12
    """
    s1 = sum(e - i for i, e in enumerate(sigma, 1) if e > i)
    s2 = sum(-e for e in sigma if e < 0)
    s3 = (oddness(sigma) - sigma.colors().count(-1)) / 2
    return s1 + s2 + s3

def oddness(sigma):
    """
    sage: sigma = SignedPermutation([2,-4,3,-1,7,-5,6])
    sage: oddness(sigma)
    1
    sage: sigma = SignedPermutation([2,-4,3,-6,7,-5,1])
    sage: oddness(sigma)
    1

    sage: sigma = SignedPermutation([-1,-2,-3,-4])
    sage: oddness(sigma)
    4
    """
    return sum(1 for b in decomposition(sigma)
               if is_odd(b.colors().count(-1)))

def decomposition(sigma):
    """
    sage: sigma = SignedPermutation([2,-4,3,-1,7,-5,6])
    sage: decomposition(sigma)
    [[2, -4, 3, -1], [3, -1, 2]]

    sage: sigma = SignedPermutation([2,-4,3,-6,7,-5,1])
    sage: decomposition(sigma)
    [[2, -4, 3, -6, 7, -5, 1]]
    """
    pi = sigma.permutation()
    summands = []
    j = 0
    for i in range(1, len(pi)):
        if max(pi[:i]) <= i:
            summand = SignedPermutation([e-j if e > 0 else e + j for e in sigma[j:i]])
            summands.append(summand)
            j = i
    summand = SignedPermutation([e-j if e > 0 else e + j for e in sigma[j:]])
    summands.append(summand)
    return summands

Created

Mar 31, 2023 at 20:59 by Martin Rubey

Updated

Mar 31, 2023 at 20:59 by Martin Rubey